Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 9.2, Problem 1P
a)
Summary Introduction
To determine: The worst possible outcome for each decision.
Introduction: The variation between the present value of the
b)
Summary Introduction
To determine: The best possible outcome for each decision.
Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).
c)
Summary Introduction
To determine: The variance of the distribution of the outcomes.
Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).
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If you want to invest in a project that cost $3.5 million. As we are unsure about the future demand, there is a 40% probability of high demand with a present value for the project $3 million. There is a 25% probability of moderate demand with a present value of $2.5 million. In addition, there is a 35% probability of low demand with a present value is $1.5 million.
Draw a decision tree for this problem. What is the expected net present value of the business? Should you invest? Explain.
Assume that you can expand the project by investing another $0.6 million after you learn the true future demand state. This would make the present value of the business $3.9 million in the high‐demand state, $3.5 million in the moderate demand state, and $1.80 million in the low demand state. Draw a decision tree to reflect the option to expand. Evaluate the alternatives. What is the net present value of the business if you consider the option to expand? How valuable is the option to expand?
Many decision problems have the following simplestructure. A decision maker has two possible decisions,1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility.
Which investment should Warren make under each of the following criteria? a. Maximax criterion.
b. Maximin criterion.
c. Maximum likelihood criterion.
d. Bayes’ decision rule.
e. The investor decides that Bayes’ decision rule is his most reliable decision criterion. He
believes that 0.1 is just about right as the prior probability of an improving economy, but is quite uncertain about how to split the remaining probabilities between a stable economy and a worsening economy. Therefore, he now wishes to do some sort of sensitivity analysis with respect to these latter two prior probabilities. If he still wants to choose the alternative from
the Bayes’ decision rule (part d):
e1. How much would be the maximum amount of the prior probability of a stable economy? e2. How much would be the minimum amount of the prior probability of a worsening economy?
Chapter 9 Solutions
Practical Management Science
Ch. 9.2 - Prob. 1PCh. 9.2 - Prob. 2PCh. 9.2 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.4 - Explain in some detail how the PrecisionTree...Ch. 9.4 - Prob. 9PCh. 9.4 - Prob. 10P
Ch. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 21PCh. 9.5 - The model in Example 9.3 has only two market...Ch. 9.6 - Prob. 26PCh. 9.6 - Prob. 27PCh. 9.6 - Prob. 28PCh. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 9 - Prob. 32PCh. 9 - Prob. 34PCh. 9 - Prob. 36PCh. 9 - Prob. 37PCh. 9 - Prob. 38PCh. 9 - Prob. 39PCh. 9 - Prob. 46PCh. 9 - Prob. 48PCh. 9 - Prob. 53PCh. 9 - Prob. 67PCh. 9 - Prob. 68PCh. 9 - Prob. 69PCh. 9 - Prob. 70PCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Prob. 76PCh. 9 - Prob. 77P
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